QUANTITATIVE
REASONING (QR) DATA
ANALYSIS
CNAS ASSESSMENT WORKSHOP
April 17th, 2015
Grazyna Badowski
9/9/2015
QR: What is it?
• One of WASC's five core competencies
• One of the Liberal Education and America's Promise
(LEAP) essential learning outcomes
• One of UOG’s ILOs
• An aspect of citizenship: How do students understand
numbers in public life?
• Habit of mind, a way of thinking.
QR: Dr. Susan Elrod
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Contrast between mathematics and QR
Mathematics
Quantitative Reasoning
Power in abstraction
Real, authentic contexts
Power in generality
Specific, particular applications
Some context dependency
Heavy context dependency
Society indenpendet
Society dependent
Apolitical
Political
Methods and algorithm
Ad hoc methods
Well-defined problems
Ill-defined problems
Approximation
Estimation is critical
Heavily disciplinary
Interdisciplinary
Problem solutions
Problems descriptions
Few opportunities to practice outside
the classroom
Many practice opportunities outside
the classroom
Predictable
Unpredictable
Source: Shavelson, R. J. (2008). Reflections on quantitative reasoning: An Assessment Perspective. In B. L. Madison & L. A. Steen. (Eds). Calculation vs.
context: Quantitative literacy and its implications for teacher education, pp 27-47. Mathematical Association of America.
Mathematical Association of America (MAA)
QR Learning Outcomes
• Interpret mathematical models such as formulas, graphs,
•
•
•
•
tables, and schematics, and draw inferences from them.
Represent mathematical information symbolically, visually,
numerically, and verbally.
Use arithmetical, algebraic, geometric and statistical
methods to solve problems.
Estimate and check answers to mathematical problems in
order to determine reasonableness, identify alternatives,
and select optimal results.
Recognize that mathematical and statistical methods
have limits.
Source: http://www.maa.org/programs/faculty-and-departments/curriculum-department-guidelinesrecommendations/quantitative-literacy/quantitative-reasoning-college-graduates#Part1
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QR at UOG
• QR is one of UOG’s ILOs.
• It was stated as: “Mastery of quantitative analysis”
• In Fall 2014, University Assessment Committee (UAC)
worked on clarifying statements for the University ILOs
Clarifying statements for QR at UOG
BEFORE: “Mastery of quantitative analysis”
NOW: Upon completion of degree, a University of Guam student will
be able to :
1.
2.
3.
4.
5.
6.
Provide accurate explanations of information presented in
mathematical forms. Make appropriate inferences based on that
information.
Convert any relevant information into various meaningful
mathematical forms (equations, graphs, diagrams, tables, words).
Identify and propose solutions for problems using quantitative tools
and reasoning using calculations.
Use the quantitative analysis of data as the basis for deep and
thoughtful judgments, drawing insightful, carefully qualified
conclusions from this work.
Explicitly describe assumptions and provide compelling rationale
for why each assumption is appropriate.
Use quantitative information in connection with the argument or
purpose of the work, present it in an effective format, and
explicates it with consistently high quality.
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9/9/2015
UOG Clarifying statements for ILOs: Example
Translate verbal problems into mathematical algorithms,
constructs valid arguments using the accepted symbolic
system of mathematical reasoning, and constructs accurate
calculations, estimates, risk analyses or quantitative
evaluations of public information through presentations,
papers or projects. (Quantitative fluency)
QR at UOG
QR in GE Learning Outcomes?
UOG students will be able to apply analytical and QR reasoning to
address complex challenges and everyday problems by:
1. Interpreting information presented in a mathematical and graphical
form;
2. Representing information in a mathematical and graphical form;
3. Effectively calculating using quantitative data;
4. Analyzing quantitative information in order to scrutinize it and draw
appropriate conclusions;
5. Evaluating the assumptions used in analyzing quantitative data
6. Communicating quantitative information in support or refutation of
an argument.
• Where in the curriculum students will be expected to gain QR skills ?
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Where in GE should we teach QR?
• Where in the curriculum students will be expected to gain QR
skills ?
•
•
•
•
•
•
•
•
•
•
•
MA110 Finite Mathematics
MA115 Introductory College Algebra
MA151 Introductory Statistics
MA161 College Algebra and Trig
MA165 PreCalculus
?
?
?
?
?
All
QR: Assessment at UOG
• Fall 2013: 3 faculty memebers: Smith, Lee, Badowski
attended WASC workshop.
• UAC tasked CNAS to take the lead in QR assessment
• QR subcommittee was created:
• Chair: Frank Camacho
• Members: Maika Vuki, Carl Swanson, Grazyna Badowski
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QR Assessment at UOG, Spring 2014
• Used the test developed by Dr. Eric Gaze, Director of the
Quantitative Reasoning at Bowdoin University.
The test has 20 multiple choice questions.
It also has five attitudinal questions.
• Assessed students at the end of Spring 2014 in MA110,
115, 151, 161A, and 165 to get some baseline data.
• Assessed seniors at the end of Spring 2014 in selected
capstone courses.
• We will track the students.
QR at UOG Spring 2014. Data analysis.
Frequency
Percentage
Male
124
49%
Female
131
51%
100-200
125
49%
300-400
128
50%
online
140
55%
paper
115
45%
SEX
LEVEL
DELIVERY
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QR at UOG Spring 2014. Data analysis.
COURSE
MA165
MA110
MA115
MA151
MA161A
BI310
CO491
MA385
CS315
MA203
BI333
BI410
CH310
CS425
MA422
NA
Total
N
6
10
4
50
25
21
8
16
21
30
14
5
24
5
14
2
255
Mean
21.7%
22.0%
27.5%
30.1%
32.6%
36.9%
38.1%
38.8%
50.0%
50.5%
54.3%
57.0%
61.3%
65.0%
67.5%
62.5%
43.0%
Std. Deviation
9.8%
9.2%
11.9%
17.9%
15.2%
16.8%
22.8%
23.0%
21.3%
22.8%
24.2%
12.0%
20.4%
23.7%
17.1%
46.0%
23.1%
QR at UOG Spring 2014. Data analysis by level.
Level
Lower
Upper
N
125
128
Mean
34.4%
51.1%
Std. Deviation
20.0%
22.7%
Level_3
100-level
200-level
300-400
N
95
30
128
Mean
29.3%
50.5%
51.1%
Std. Deviation
16.0%
22.8%
22.7%
Note: 200-level students were mostly calculus students
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QR at UOG Spring 2014. Data analysis.
MA085
no
yes
Total
p-value=0
N
172
83
255
Mean
49.9%
28.5%
43.0%
Std. Deviation
22.9%
15.8%
23.1%
Students who reported having taken a developmental mathematics
course scored significantly lower than those who did not require
developmental mathematics.
MA151
N
Mean
Std. Deviation
No
166
41.5%
23.5%
Yes
89
45.6%
22.3%
P-value=.18
Students who reported having taken MA151 Basic Statistics course
scored higher than those who did not although the difference is not
statistically significant.
QR at UOG Spring 2014. Data analysis.
MAJOR
Math/Science
Social Science
Humanities
Engineering/Technology
Other
Total
N
135
33
10
29
21
228
Mean
47.7%
31.5%
34.5%
44.7%
35.7%
43.3%
Std. Deviation
23.4%
19.7%
19.1%
21.8%
23.8%
23.3%
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QR at UOG Spring 2014. Data analysis by question.
Percent Correct
80
70
60
50
40
30
20
10
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
QR at UOG Spring 2014. Data analysis.
Percent Correct by level
90
80
70
60
50
40
30
20
10
0
1
2
3
4
5
6
7
8
9
10
Lower
11
12
13
14
15
16
17
18
19
20
Upper
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QR at UOG Spring 2014. Data analysis.
80%
70%
60%
50%
40%
30%
20%
10%
0%
1
2
3
4
5
6
7
8
9
10
No MA151
11
12
13
14
15
16
17
18
19
20
Took MA151
Comparison of UOG QR Data with other Institutions
Institution
N
Mean %
St. Dev%
2-Year
273
39.3
20.2
Selective 4-year
1088
59.7
22.8
Non-selective 4-year
811
30.1
17.9
UOG
255
43.0
23.1
Total:
2,427
43.0
22.8
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Other QR Student Learning Outcomes
1. View mathematics with heightened interest, increased
confidence, and less anxiety as a result of their
educational experiences.
2. Regard mathematics as a way to think, reason and
conceptualize, not simply as a set of techniques.
3. Understand and appreciate the connections between
mathematics and a variety of quantitative and nonquantitative disciplines.
Attitudes
Numerical information is useful in everyday life
56.5%
Strongly Agree
Numbers are not necessary for most situations.
23.9%
Strongly Disagree
38.8%
Quantitative information is vital for accurate decisions. Strongly Agree
Understanding numbers is as important in daily life as 63.1%
reading and writing.
Strongly Agree
It is a waste of time to learn information containing a 53.7%
lot of numbers.
Strongly Disagree
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Relationship between attitude score and QR test score.
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